Transmission of waves across atomic step discontinuities in discrete nanoribbon structures

Abstract

Scalar wave propagation across a semi-infinite step or step-like discontinuity on any one boundary of the square lattice waveguides is considered within nearest-neighbour interaction approximation. An application of the Wiener-Hopf method does yield an exact solution of the discrete scattering problem, using which, as the main result of the paper, the transmission coefficients for energy flux are obtained. It is assumed that a wave mode is incident from either side of the step and the question addressed is what fraction of incident energy is transmitted across the atomic step discontinuity. A total of ten configurations are presented that arise due to various placements of discrete Dirichlet and Neumann boundary conditions on the waveguide. Numerical illustrations of a measure of conductance are provided.

References in corpus (8)

• Quantized thermal conductance of dielectric quantum wires
• Effect of phonon scattering by surface roughness on the universal thermal conductance
• Anti-plane surface waves in media with surface structure: discrete vs. continuum model
• Reflection and transmission of waves in surface-disordered waveguides
• Wave transmission across surface interfaces in lattice structures
• Discrete scattering by a pair of parallel defects
• Wave scattering on lattice structures involving array of cracks
• Kinematically restricted phonon transmission in partly-unzipped tubes of square and triangular lattices